Allardyce awaiting Fletcher decision
Fletcher is a target for West Brom head coach Tony Pulis, while Valencia have also been linked with the long-serving United midfielder.
Allardyce on Friday revealed that Fletcher is assessing his options just over a week before the transfer window closes.
The West Ham boss said: "Darren Fletcher has got several clubs interested in him, so it is up to him where he wants to go."
The Premier League high-fliers face a tricky trip to League One promotion-hopefuls Bristol City in the fourth round of the FA Cup on Sunday.
West Ham beat Everton in a dramatic penalty shoot-out to stay in the competition last week, and Allardyce has no plans to rotate his squad as he eyes a long cup run.
He said: "Bristol City are doing well at the moment in League One. Several Premier League teams have struggled against lower league opposition.
"We're all fit and well apart from James Collins and Diafra Sakho. So we have a strong squad to face Bristol City.
"I don't have a problem playing my full strength team as we've got a full week until our next league game.
"We put a lot of energy into the Everton tie, over two games, so we don't want that to be in vain. We want to win on Sunday."